I'm opening this issue to start a discussion on how we may handle a case where we want to have a field discontinuity across a geometric interface. This is the case for some of the particle calculations where a change of materials will cause a discontinuity.
For a standard DG type calculation, we would just add DOFs that are associated with the dimension of the model rather than having them associated with the interface dimension (face in 3D, edge in 2D).
For this use-case, we only want additional DOFs on the geometric boundaries.